1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 55         
 56         /**************************** Circle.sas ****************************/
 57         title 'Try to fit a non-identified model';
 58         title2 'Jerry Brunner:  Student Number 999999999';
 59         
 60         data Bizarre;
 61              infile '/folders/myfolders/431s17/Circle.data.txt' firstobs=2 ;  /* Skipping the header */
 62              input id Y1-Y4;
 63         
 64         
 
 NOTE: The infile '/folders/myfolders/431s17/Circle.data.txt' is:
       Filename=/folders/myfolders/431s17/Circle.data.txt,
       Owner Name=root,Group Name=vboxsf,
       Access Permission=-rwxrwx---,
       Last Modified=30Jan2015:16:40:51,
       File Size (bytes)=15311
 
 NOTE: 250 records were read from the infile '/folders/myfolders/431s17/Circle.data.txt'.
       The minimum record length was 59.
       The maximum record length was 59.
 NOTE: The data set WORK.BIZARRE has 250 observations and 5 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.05 seconds
       cpu time            0.01 seconds
       
 65         proc calis pshort nostand vardef=n pcorr;
 
 66          title3 'True beta1 = 0.7071068, beta2 = -0.7071068, psi1 = psi2 = 1';
 67          title4 'With psi1 neq psi2, fails parameter count rule';
 68              var Y1 Y2;  /* Declare observed variables */
 69              lineqs
 70                 /* Latent variables must begin with F for Factor.
 71                    Error terms must begin with e or d (for disturbance) */
 72                 Y1 = beta1*F1 + beta2*F2 + epsilon1,
 73                 Y2 = beta1*F1 + beta2*F2 + epsilon2;
 74              variance                   /* Declare variance parameters. */
 75                 epsilon1 = psi1, epsilon2 = psi2,
 76                 F1 = 1, F2 = 1;
 77              cov
 78                 F1 F2 = 0;
 79              /* Other unmentioned covariances are assumed zero. */
 80              /* If no means or intercepts are given, model is assumed to
 81                 be in centered form. Unmentioned means and intercepts are
 82                 re-parameterized and disappear from the likelihood. */
 83         
 
 WARNING: The estimation problem is not identified: There are more parameters to estimate ( 4 ) than the total number of mean and 
          covariance elements ( 3 ).
 NOTE: Convergence criterion (GCONV2=0) satisfied.
 NOTE: The Moore-Penrose inverse is used in computing the covariance matrix for parameter estimates.
 WARNING: Standard errors and t values might not be accurate with the use of the Moore-Penrose inverse.
 WARNING: Critical N is not computable for df= -1.
 NOTE: PROCEDURE CALIS used (Total process time):
       real time           2.75 seconds
       cpu time            0.41 seconds
       
 84         proc calis pshort nostand vardef=n pcorr;
 
 85          title3 'True beta1 = 0.7071068, beta2 = -0.7071068, psi1 = psi2 = 1';
 86          title4 'Passes parameter count rule with psi1=psi1=psi';
 87              var Y1 Y2;  /* Declare observed variables */
 88              lineqs
 89                 /* Latent variables must begin with F for Factor.
 90                    Error terms must begin with e or d (for disturbance) */
 91                 Y1 = beta1*F1 + beta2*F2 + epsilon1,
 92                 Y2 = beta1*F1 + beta2*F2 + epsilon2;
 93              variance                   /* Declare variance parameters. */
 94                 epsilon1 = psi, epsilon2 = psi,
 95                 F1 = 1, F2 = 1;
 96              cov
 97                 F1 F2 = 0;
 98         
 
 NOTE: Convergence criterion (ABSGCONV=0.00001) satisfied.
 NOTE: The Moore-Penrose inverse is used in computing the covariance matrix for parameter estimates.
 WARNING: Standard errors and t values might not be accurate with the use of the Moore-Penrose inverse.
 WARNING: Critical N is not computable for df= 0.
 NOTE: PROCEDURE CALIS used (Total process time):
       real time           0.38 seconds
       cpu time            0.35 seconds
       
 99         proc calis pshort nostand vardef=n pcorr;
 
 100         title3 'True beta1 = 0.7071068, beta2 = -0.7071068, psi1 = psi2 = 1';
 101         title4 'Psi1 neq psi2 again, start at beta1 = -0.9824205, beta2=0';
 102             var Y1 Y2;  /* Declare observed variables */
 103             lineqs
 104                /* Latent variables must begin with F for Factor.
 105                   Error terms must begin with e or d (for disturbance) */
 106                Y1 = beta1(-0.9824205)*F1 + beta2(0)*F2 + epsilon1,
 107                Y2 = beta1(-0.9824205)*F1 + beta2(0)*F2 + epsilon2;
 108             variance                   /* Declare variance parameters. */
 109                epsilon1 = psi1(0.75731), epsilon2 = psi2(1.19528),
 110                F1 = 1, F2 = 1;
 111             cov
 112                F1 F2 = 0;
 113        
 
 WARNING: The estimation problem is not identified: There are more parameters to estimate ( 4 ) than the total number of mean and 
          covariance elements ( 3 ).
 NOTE: Convergence criterion (ABSGCONV=0.00001) satisfied.
 NOTE: The Moore-Penrose inverse is used in computing the covariance matrix for parameter estimates.
 WARNING: Standard errors and t values might not be accurate with the use of the Moore-Penrose inverse.
 NOTE: The standard error estimate of beta2 is zero or very close to zero.
 WARNING: Critical N is not computable for df= -1.
 NOTE: PROCEDURE CALIS used (Total process time):
       real time           0.34 seconds
       cpu time            0.32 seconds
       
 114        proc calis pshort nostand vardef=n pcorr;
 
 115         title3 'True beta1 = beta2 = 0, psi1 = psi2 = 1';
 116         title4 'Fails parameter count rule';
 117             var Y3 Y4;  /* Declare observed variables */
 118             lineqs
 119                /* Latent variables must begin with F for Factor.
 120                   Error terms must begin with e or d (for disturbance) */
 121                Y3 = beta1*F1 + beta2*F2 + epsilon1,
 122                Y4 = beta1*F1 + beta2*F2 + epsilon2;
 123             variance                   /* Declare variance parameters. */
 124                epsilon1 = psi1, epsilon2 = psi2,
 125                F1 = 1, F2 = 1;
 126             cov
 127                F1 F2 = 0;
 128        
 129        
 130        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 WARNING: The estimation problem is not identified: There are more parameters to estimate ( 4 ) than the total number of mean and 
          covariance elements ( 3 ).
 WARNING: Standard errors and t values might not be accurate with the use of the Moore-Penrose inverse.
 WARNING: Critical N is not computable for df= -1.
 142